# Coordinate system problems and answers

Recent questions in Alternate coordinate systems
Alternate coordinate systems

### Solve the following systems of inequalities graphically on the set of axes below.The state the following coordinates of a point in the solution say $$\displaystyle{y}\leq{x}+{6}$$ $$\displaystyle{y}\succ{\frac{{{3}}}{{{2}}}}{x}-{4}$$

Alternate coordinate systems

### Consider the following system. $$\begin{cases}{y}={30}-{x}\\{2}{y}=-{x}^{{{2}}}+{16}{x}-{12}\end{cases}$$

Alternate coordinate systems

### This question has to do with binary star systems, where 'i' is the angle of inclination of the system. Calculate the mean expectation value of the factor $$\displaystyle{{\sin}^{{{3}}}}$$ i, i.e., the mean value it would have among an ensemble of binaries with random inclinations. Find the masses of the two stars, if $$\displaystyle{{\sin}^{{{3}}}}$$ i has its mean value. Hint: In spherical coordinates, $$\displaystyle{\left(\theta,\phi\right)}$$, integrate over the solid angle of a sphere where the observer is in the direction of the z-axis, with each solid angle element weighted by $$\sin^3 \theta$$. $$\displaystyle{v}_{{{1}}}={100}{k}\frac{{m}}{{s}}$$ $$\displaystyle{v}_{{{2}}}={200}{k}\frac{{m}}{{s}}$$ Orbital period $$\displaystyle={2}$$ days $$\displaystyle{M}_{{{1}}}={5.74}{e}^{33}{g}$$ $$\displaystyle{M}_{{{2}}}={2.87}{e}^{33}{g}$$

Alternate coordinate systems

### Discuss: Different Coordinate Systems As was noted in the overview of the chapter, certain curves are more naturally described in one coordinate system than in another. In each of the following situations, which coordinate system would be appropriate: rectangular or polar? Give reasons to support your answer. a) You need to give directions to your house to a taxi driver. b) You need to give directions to your house to a homing pigeon.

Alternate coordinate systems

### We can describe the location of a point in the plane using different ________ systems. The point P shown in the figure has rectangular coordinates ( _ , _ ) and polar coordinates ( _, _).

Alternate coordinate systems

### Systems of Inequalities Graph the solution set of the system if inequalities. Find the coordinates of all vertices, and determine whether the solution set is bounded. $$\begin{cases}y < 9 - x^{2}\\y \geq x + 3 \end{cases}$$

Alternate coordinate systems

### Solving Systems Graphically- One Solution Find or create an example of a system of equations with one solution. Graph and label the lines on a coordinate plane. Provide their equations. State the accurate solution to the system.

Alternate coordinate systems

### a) What coordinate system is suggested to be used when seeing the integrand $$\displaystyle{\left({x}^{{{2}}}+{y}^{{{2}}}\right)}^{{\frac{{5}}{{2}}}}$$, cylindrical or Cartesian? b) List the conversion factors for rectangular to cylindrical coordinate systems.

Alternate coordinate systems

### Convert between the coordinate systems. Use the conversion formulas and show work. spherical: $$\displaystyle{\left({8},{\frac{{\pi}}{{{3}}}},{\frac{{\pi}}{{{6}}}}\right)}$$ Change to cylindrical.

Alternate coordinate systems

### Below are various vectors in cartesian, cylindrical and spherical coordinates. Express the given vectors in two other coordinate systems outside the coordinate system in which they are expressed $$a) \overrightarrow{A}(x,y,z)=\overrightarrow{e}_{x}$$ $$d)\overrightarrow{A}(\rho, \phi, z)= \overrightarrow{e}_{\rho}$$ $$g)\overrightarrow{A}(r, \theta, \phi)=\overrightarrow{e}_{\theta}$$ $$j)\overrightarrow{A}(x,y,z)=\frac{-y\overrightarrow{e}_{x}+x\overrightarrow{e}_{y}}{x^{2}+y^{2}}$$

Alternate coordinate systems

### Given point $$\displaystyle{P}{\left(-{2},{6},{3}\right)}$$ and vector $$\displaystyle{B}={y}{a}_{{{x}}}+{\left({x}+{z}\right)}{a}_{{{y}}}$$, Express P and B in cylindrical and spherical coordinates. Evaluate A at P in the Cartesian, cylindrical and spherical systems.

Alternate coordinate systems

### How are triple integrals defined in cylindrical and spherical coor-dinates? Why might one prefer working in one of these coordinate systems to working in rectangular coordinates?

Alternate coordinate systems

### The Cartesian coordinates of a point are given. a) $$(2,-2)$$ b) $$(-1,\sqrt{3})$$ Find the polar coordinates $$(r,\theta)$$ of the point, where r is greater than 0 and 0 is less than or equal to $$\theta$$, which is less than $$2\pi$$ Find the polar coordinates $$(r,\theta)$$ of the point, where r is less than 0 and 0 is less than or equal to $$\theta$$, which is less than $$2\pi$$

Alternate coordinate systems

### For the cuboid below: a. write down the coordinates of point B. b. write down the coordinates of point A. c. find the coordinates of the midpoint, M, of the diagonal [AO] of the cuboid.

Alternate coordinate systems

### Find the value of x or y so that the line passing through the given points has the given slope. (9, 3), (-6, 7y), $$m = 3$$

Alternate coordinate systems

### To plot: Thepoints which has polar coordinate $$\displaystyle{\left({2},\frac{{{7}\pi}}{{4}}\right)}$$ also two alternaitve sets for the same.

Alternate coordinate systems

### The system of equation $$\begin{cases}2x + y = 1\\4x +2y = 3\end{cases}$$ by graphing method and if the system has no solution then the solution is inconsistent. Given: The linear equations is $$\begin{cases}2x + y = 1\\4x +2y = 3\end{cases}$$

Alternate coordinate systems

### What are polar coordinates? What equations relate polar coordi-nates to Cartesian coordinates? Why might you want to change from one coordinate system to the other?

Alternate coordinate systems